MIX:  Bayesian inference for mixture models.

The 'mix' programs implement Bayesian models for multivariate
probability or probability density estimation that are based on finite
or countably infinite mixtures.  The countably infinite mixture models
are equivalent to Dirichlet process mixtures.

Each component of the mixture defines a joint probability or
probability density for a set of target variables.  At present, the
targets must either all be binary or all be real-valued.  For binary
data, the targets are independent in the component distributions, with
a "1" having some specified probability.  For real-valued data, the
targets are also independent in each of the component densities, each
having a Gaussian distribution with some specified mean and standard
deviation.  The full distribution defined by the model is a mixture of
these component distributions, with the weight of each component in
the mixture being given by a set of component probabilities.

The parameters of the component distributions (eg, the means and
standard deviations for Gaussians) are given prior distributions,
which may depend on "hyperparameters" that are themselves given
priors.  The mixing proportions are given a symmetric Dirichlet prior,
with specified concentration parameter.  In this implementation, these
mixing proportions are not explicitly represented; all inference is
instead done with the proportions integrated out.  Sampling from the
posterior distribution for the other parameters of the components and
the hyperparameters is done using Markov chain methods.  The resulting
sample from the posterior can then be used to make predictions for
future cases.

The facilities supported by these programs are presently a bit
rudimentary; mix-extensions.doc gives a list of things that could be
done, but aren't yet.

            Copyright (c) 1997 by Radford M. Neal